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---
:name: dlarrk
:md5sum: 4e0b3e510031faaddb890af5e08e89a2
:category: :subroutine
:arguments:
- n:
:type: integer
:intent: input
- iw:
:type: integer
:intent: input
- gl:
:type: doublereal
:intent: input
- gu:
:type: doublereal
:intent: input
- d:
:type: doublereal
:intent: input
:dims:
- n
- e2:
:type: doublereal
:intent: input
:dims:
- n-1
- pivmin:
:type: doublereal
:intent: input
- reltol:
:type: doublereal
:intent: input
- w:
:type: doublereal
:intent: output
- werr:
:type: doublereal
:intent: output
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE DLARRK( N, IW, GL, GU, D, E2, PIVMIN, RELTOL, W, WERR, INFO)\n\n\
* Purpose\n\
* =======\n\
*\n\
* DLARRK computes one eigenvalue of a symmetric tridiagonal\n\
* matrix T to suitable accuracy. This is an auxiliary code to be\n\
* called from DSTEMR.\n\
*\n\
* To avoid overflow, the matrix must be scaled so that its\n\
* largest element is no greater than overflow**(1/2) *\n\
* underflow**(1/4) in absolute value, and for greatest\n\
* accuracy, it should not be much smaller than that.\n\
*\n\
* See W. Kahan \"Accurate Eigenvalues of a Symmetric Tridiagonal\n\
* Matrix\", Report CS41, Computer Science Dept., Stanford\n\
* University, July 21, 1966.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* N (input) INTEGER\n\
* The order of the tridiagonal matrix T. N >= 0.\n\
*\n\
* IW (input) INTEGER\n\
* The index of the eigenvalues to be returned.\n\
*\n\
* GL (input) DOUBLE PRECISION\n\
* GU (input) DOUBLE PRECISION\n\
* An upper and a lower bound on the eigenvalue.\n\
*\n\
* D (input) DOUBLE PRECISION array, dimension (N)\n\
* The n diagonal elements of the tridiagonal matrix T.\n\
*\n\
* E2 (input) DOUBLE PRECISION array, dimension (N-1)\n\
* The (n-1) squared off-diagonal elements of the tridiagonal matrix T.\n\
*\n\
* PIVMIN (input) DOUBLE PRECISION\n\
* The minimum pivot allowed in the Sturm sequence for T.\n\
*\n\
* RELTOL (input) DOUBLE PRECISION\n\
* The minimum relative width of an interval. When an interval\n\
* is narrower than RELTOL times the larger (in\n\
* magnitude) endpoint, then it is considered to be\n\
* sufficiently small, i.e., converged. Note: this should\n\
* always be at least radix*machine epsilon.\n\
*\n\
* W (output) DOUBLE PRECISION\n\
*\n\
* WERR (output) DOUBLE PRECISION\n\
* The error bound on the corresponding eigenvalue approximation\n\
* in W.\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: Eigenvalue converged\n\
* = -1: Eigenvalue did NOT converge\n\
*\n\
* Internal Parameters\n\
* ===================\n\
*\n\
* FUDGE DOUBLE PRECISION, default = 2\n\
* A \"fudge factor\" to widen the Gershgorin intervals.\n\
*\n\n\
* =====================================================================\n\
*\n"
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